For pitchers, strikeouts are usually seen as negatively and significantly affecting the runs they allow. But on the batting side, they are often seen as being no worse than any other out (and certainly preferable to grounding into a double play). The negative run value of regular outs and strikeouts was found to be about the same in an article about "extrapolated runs" in the 1999 Big Bad Baseball Annual.
I also looked at all players with 5000+ (plate appearances) PAs from 1913-2005 and found the correlation between their offensive winning percentage (OWP-a Bill James stat that says what your team's winning percentage would be if each of the nine batters was identical and you gave up an average number of runs) and their strikeout rate relative to the league average was .316. That suggests the more you strikeout, the better hitter you are.
But, many power hitters strikeout alot and since power hitting helps your OWP, it is not too big a surprise that we see this positive correlation (strikeouts per se are not in the formula for OWP). Since any out, strikeouts included will lower your OWP, it is probably the case that the power hitters more than make up for the negative value of their strikeouts with their power (and they may get on base alot which also helps their OWP). So I segmented this group of players into the top 50 and bottom 50 in isolated power relative to the league average (isolated power is SLG - AVG).
The correlation between the top 50 all-time in relative isolated power and relative strikeout rate is -.166. For the bottom 50 all-time in relative isolated power it is -.23. I also looked at current players. For all batters with 3000+ PAs from 1996-2005, the correlation between relative strikeout rate and OWP is .28. For top 50 in relative isolated power, the correlation is -.26. For the bottom 50, it is -.13. So, if we try to classify hitters, there may be a negative relationship between strikeouts and a hitter's effectiveness. Within the group of the best power hitters, strikeouts are negatively correlated with performance. Same for the least powerful hitters. The effect is there, even if it is not very strong.
I also looked to see what happened when players reduced their strikeout rate. The players were anyone who had 400 PAs during any of the seasons from 2002-05. The following table shows the correlation between the change in a player's strikeout rate and the change in the other stats going from season to season. I used two rates, strikeouts per AB and strikeouts per PA. Here they are:
So, for example, the correlation between the change in a players strikeouts per AB and change in his batting average going from 2002-3 was -.261. If strikeouts went down, then AVG went up (only players who had 400+ PAs in each season were used). Most of these correlations were statistically significant. But how strong is the effect? And is it there just because strikeouts going down simply means that outs are going down?
Using the data from the 2002-3 seasons, I ran a regression with change in AVG being the dependent variable and change in strikeouts per AB being the independent variable.
The equations was:
AVGChange = -.00036 - .274*(SO/AB)Change
This means that if a player cut his strikeouts down by 100, his hits would go up by 27.4. That is like saying on his additional ABs when he does not strikeout, he bats .274. This may not be impressive because for all of these players over the 2002-3 seasons, they already bat about .336 when they don't strikeout. Also, the r-squared was only .068, meaning that the regression explains only about 6.8% of the variation in AVGChange. So if there is any negative side to striking out, it is probably not too large.